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Unformatted text preview: Solution HW 7
Problem 1
a) For the 1st order system, the static sensitivity and time constant will fully characterize
the system.
b) Static sensitivity:
From the step response plot for the 1st order system, the response is 10.00063V when
t=0.1s. So the time constant is about 0.1s.
Problem 2.
a) The system is 2nd order system, since it exhibits some oscillation around the steady
state.
b) Static sensitivity:
c) The oscillation period
is about 0.065sec. When we determine , we estimate the
time instant at which the step response is equal to the steady state output.
d) The %OS method will be used to estimate the damping ratio, since the maximum
overshoot is marked in the step response. e) The natural frequency is a) The frequency response function of this system is The differential equation is Substituting the numerical value into the above equation, we get Problem 3
Problem is solved by reading values off the graphs:
a) gain = 40 dB so K=100.
b) ωn is 50 rad/sec from the phase plots (90 deg)
c) Amplification method: Half power method: Slope of phase angle method: ...
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This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue UniversityWest Lafayette.
 Fall '07
 MERKLE

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